CN107423257B - Method for solving maximum power point parameter of solar cell - Google Patents

Method for solving maximum power point parameter of solar cell Download PDF

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CN107423257B
CN107423257B CN201710209412.XA CN201710209412A CN107423257B CN 107423257 B CN107423257 B CN 107423257B CN 201710209412 A CN201710209412 A CN 201710209412A CN 107423257 B CN107423257 B CN 107423257B
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maximum power
power point
solar cell
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汪石农
金震妮
徐杰
郑刘康
汪林
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Anhui Polytechnic University
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Abstract

The invention discloses a method for solving parameters of a maximum power point of a solar cell, which is characterized by comprising the following steps: the method comprises the following steps: the method comprises the following steps: establishing an ideal circuit model and a general circuit model of the solar cell; step two: calculating a maximum power point parameter under an ideal circuit model; step three: in a general equivalent circuit model, a maximum power point parameter solving formula under the general equivalent circuit model is deduced according to a maximum power point parameter under an ideal circuit model and kirchhoff's law. The invention builds the mathematical relationship among the maximum power point voltage, the maximum power point current, the maximum power and each constant and parameter through strict theoretical derivation, avoids the transcendental equation containing index in the general solar cell model, has definite relationship among variables, and does not need iterative algorithm in the solving process.

Description

Method for solving maximum power point parameter of solar cell
Technical Field
The invention belongs to the field of solving of a maximum power point of a solar cell, and particularly relates to an engineering solving method for voltage, maximum power point current and maximum power of the maximum power point of the solar cell.
Background
With the gradual decrease of various fossil energy sources on the earth, various renewable energy sources become the direction of disputed development of various countries. The solar energy is one of renewable energy sources with great development potential due to inexhaustible solar energy, cleanness and no pollution. However, in the occasions of solar cell power generation system design, micro-grid system simulation, solar cell maximum power point tracking and the like, engineering parameters related to the solar cell, especially related parameters such as maximum power point voltage, maximum power point current and maximum power, need to be obtained.
At present, a solar cell engineering parameter solving method is mainly to perform mathematical modeling on a solar cell in engineering software such as Matlab, Maple and Mathemica and then solve the problem through a Newton iteration method and related programs, and the whole process is complicated, inconvenient to solve and ambiguous in relation between variables. Subsequently, the relevant scholars improve the mathematical model of the solar cell to establish a relatively simple engineering model, and solve some parameters in the model to give an empirical formula, but the method still needs a newton iteration method, and the relevant empirical formula is given without corresponding theoretical support.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides the method for solving the maximum power point parameter of the solar cell, which has the advantages of direct solution, no need of iterative algorithm, clear variable relation and engineering feasibility, and the maximum power point parameter solving formula is solved by the method so as to simplify the solution.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for solving parameters of a maximum power point of a solar cell is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing an ideal circuit model and a general circuit model of the solar cell;
step two: calculating a maximum power point parameter under an ideal circuit model;
step three: in a general equivalent circuit model, a maximum power point parameter solving formula under the general equivalent circuit model is deduced according to a maximum power point parameter under an ideal circuit model and kirchhoff's law.
In the first step, the mathematical expression of the ideal circuit model of the solar cell is as follows:
Figure BDA0001260645250000021
the mathematical expression of a general equivalent circuit model is:
Figure BDA0001260645250000022
in the formula: i isideal、VidealRespectively outputting current and voltage of the solar cell under an ideal circuit model; I. v is the output current and voltage of the solar cell under the general circuit model respectively; i isphIs the photo-generated current of the solar cell; i isoIs a reverse saturation current; q is the charge amount of one electron; k is the boltzmann constant; t is the temperature of the solar cell; n is an ideal factor for a solar cell; rs、RshThe resistor is a series and parallel circuit resistor inside a solar cell and is mainly used for representing current loss inside the cell.
In the second step, the method for solving the maximum power point parameter under the ideal circuit model comprises the following steps: and (3) derivation is carried out on the mathematical expression of the solar cell ideal circuit model to obtain the inverse relation of the output current of the solar cell with respect to the voltage under the ideal model:
Figure BDA0001260645250000023
the derivative of the current output by the solar cell with respect to voltage under an ideal circuit model is equal to the inverse of the ratio of the short circuit current to the open circuit voltage of the solar cell at the maximum power point position of the solar cell:
Figure BDA0001260645250000031
wherein Isc、VocShort circuit current and open circuit voltage corresponding to an ideal solar cell; thus, under an ideal model, the maximum power point voltage is obtained:
Figure BDA0001260645250000032
obtaining the current at the maximum power point under the ideal model according to the relation between the output voltage and the current of the solar battery under the ideal model:
Figure BDA0001260645250000033
short-circuit current IscPhoto-generated current I with solar cellphThe relationship between them is: i issc＝Iph(ii) a Open circuit voltage VocPhoto-generated current I with solar cellphThe relationship between them is:
Figure BDA0001260645250000034
in the third step, when the ideal circuit model is at the maximum power point, the general equivalent circuit is also at the maximum power point, and in the general equivalent circuit of the solar cell, the maximum power point current and the maximum power point voltage under the ideal model are combined and simultaneously the kirchhoff law is utilized to obtain the maximum power point voltage V under the general equivalent modelmppMaximum power point current ImppAnd maximum power PmppRespectively as follows:
Figure BDA0001260645250000035
Figure BDA0001260645250000036
Pmpp＝Vmpp·Impp。
further comprises the following steps: simplifying a maximum power point parameter solving formula obtained under a general equivalent circuit model, neglecting a secondary part of the maximum power point parameter solving formula, and deducing an approximate calculation formula of maximum power point voltage and current under an ideal model;
step five: maximum power point voltage V under standard test condition of solar cellmpp_refAnd maximum power point current Impp_refSolving the formula and ideal from the parameters of the general equivalent circuit modelAnd obtaining a maximum power point current and voltage approximate calculation formula under the model to obtain a maximum power point parameter approximate estimation formula under a general equivalent circuit model.
Photo-generated current I of solar cellphAnd reverse saturation current IoThe calculation formula is respectively:
Figure BDA0001260645250000041
Figure BDA0001260645250000042
Iph_ref、Voc_refshort-circuit current and open-circuit voltage, mu, of the solar cell under standard test conditionsI、μVRespectively the short-circuit current temperature coefficient and the open-circuit voltage temperature coefficient of the solar cell, and the temperature is T under the standard test conditionrThe intensity of sunlight is Sref；
Photo-generated current IphReverse saturation current IoThe approximate calculation formula of the maximum power point voltage and the current under the ideal model obtained by substituting the calculation formula into the maximum power point voltage and current calculation formula under the ideal model is respectively as follows:
Figure BDA0001260645250000043
Figure BDA0001260645250000051
in the fifth step, the maximum power point parameter approximate estimation formula under the general equivalent circuit model obtained by the general equivalent circuit model parameter solving formula and the maximum power point current voltage approximate calculation formula under the ideal model is respectively as follows:
Figure BDA0001260645250000052
Figure BDA0001260645250000053
Pmpp＝Vmpp·Impp。
compared with the prior art, the invention has the following advantages:
(1) the method establishes mathematical relations among the maximum power point voltage, the maximum power point current, the maximum power and each constant and parameter through strict theoretical derivation, avoids an transcendental equation containing indexes in a general solar cell model, has clear relation among variables, and does not need an iterative algorithm in the solving process.
(2) According to the method, an approximate linear estimation formula is given on the basis of a maximum power point parameter accurate calculation formula through strict theoretical derivation, and the influence of external factors such as the temperature of the solar cell and the sunlight intensity on the maximum power point parameter is reflected visually. Meanwhile, the approximate linear estimation formula avoids more exponential and logarithmic operations, and the engineering is convenient to realize.
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The description includes the following figures, the contents shown are respectively:
FIG. 1 illustrates a step of solving the maximum power point parameter of the solar cell according to the present invention;
FIG. 2 is a solar cell equivalent circuit model;
FIG. 3 is a graph of the I-V relationship of a solar cell.
Detailed Description
The following detailed description of the embodiments of the present invention will be given with reference to the accompanying drawings for a purpose of helping those skilled in the art to more fully, accurately and deeply understand the concept and technical solution of the present invention and to facilitate its implementation.
As shown in fig. 1, a schematic diagram of a solar cell parameter solving process according to the present invention is shown;
step S1, deriving the maximum power point voltage V under the ideal circuit model according to the ideal circuit model of the solar cell and the relevant characteristics of the maximum power point of the solar cellmpp_idealAnd maximum power point current Impp_ideal。
The method specifically comprises the following steps: establishing an ideal circuit model and a general circuit model of the solar cell;
step two: calculating the maximum power point parameter, i.e. the maximum power point voltage V, under an ideal circuit modelmpp_idealAnd maximum power point current Impp_ideal；
The calculation derivation process is as follows:
as shown in fig. 2, the equivalent circuit model of the solar cell is shown, wherein an ideal circuit model of the solar cell is shown in a dashed line box, so that mathematical expressions that can be used to establish the ideal circuit model and the general equivalent circuit model of the solar cell are respectively:
Figure BDA0001260645250000061
Figure BDA0001260645250000062
in the formulae (1) and (2), Iideal、VidealRespectively, the output current and voltage of the ideal solar cell; I. v is the output current and voltage of the common solar cell respectively; i isphIs the photo-generated current of the solar cell; i isoIs a reverse saturation current; q is the charge amount of one electron; k is the boltzmann constant; t is the temperature of the solar cell; n is an ideal factor for a solar cell; rs、RshThe circuit resistors are series and parallel circuit resistors inside the solar cell and are mainly used for representing current loss inside the cell; rLThe load resistor is externally connected with the solar battery.
Data expression (1) for an ideal circuit model with respect to VidealThe derivation is as follows:
Figure BDA0001260645250000071
in addition, when the solar cell is at the maximum power point, the following properties are provided:
Figure BDA0001260645250000072
in the formula (4) Isc、VocFor the short-circuit current and the open-circuit voltage corresponding to an ideal solar cell, the corresponding expressions are respectively formula (5) and formula (6):
Isc＝Iphformula (5)
Figure BDA0001260645250000073
Formula (4) represents
Figure BDA0001260645250000074
At Videal＝Vmpp_idealWhen taking a value of
Figure BDA0001260645250000075
The maximum power point voltage V under the ideal circuit model can be calculated by substituting the point value into the formula (3)mpp_idealComprises the following steps:
Figure BDA0001260645250000076
the maximum power point current I under an ideal circuit model can be obtained by the formula (7) and the formula (1)mpp_idealComprises the following steps:
Figure BDA0001260645250000077
step S2, deducing the maximum power point voltage V of the solar battery according to a maximum power point parameter calculation formula under an ideal circuit model, a solar battery general equivalent circuit model and kirchhoff' S theoremmppMaximum power point current ImppAnd maximum power PmppThe precise calculation formula of (2). Namely, the third step: in a general equivalent circuit model, a maximum power point parameter solving formula under the general equivalent circuit model is deduced according to a maximum power point parameter under an ideal circuit model and kirchhoff's law.
The method comprises the following specific steps:
solar electricity as shown in fig. 3The I-V relation curve of the ideal circuit model of the cell and the general equivalent circuit model can obviously show that the two curves are obviously not overlapped near the maximum power point, so the maximum power point voltage V under the ideal circuit model can not be used in practicempp_idealAnd maximum power point current Impp_idealReplace the maximum power point voltage V under the general equivalent circuit modelmppAnd maximum power point current Impp。
Because of R in the solar cells<<RshThrough the theory of maximum power transmission in the circuit, it can be found that when the ideal circuit model is at the maximum power point, the general equivalent circuit model is also at the maximum power point. Therefore, in the general equivalent circuit of fig. 2, the maximum power point voltage V under the general equivalent circuit model of the solar cell can be obtained by using kirchhoff's law in combination with the expressions (7) and (8)mppMaximum power point current ImppAnd maximum power Pmpp；
The relationship satisfied by the current and voltage in kirchhoff's law can be derived as:
Figure BDA0001260645250000081
Figure BDA0001260645250000082
Pmpp＝Vmpp·Imppformula (11)
The formula (9), the formula (10) and the formula (11) are maximum power point parameter calculation formulas under a general equivalent circuit model of the solar cell, and it can be seen that no transcendental equation is included, so that an iterative algorithm is not needed during solution, and the solution is simple.
The maximum power point parameter calculation formula under the general equivalent circuit model is further simplified to obtain an approximate relation formula of the maximum power point parameter, the illumination intensity S and the temperature T of the solar cell.
Step S3, neglecting the secondary part of the maximum power point parameter calculation formula under the ideal circuit model, and calculating the maximum power pointPressure Vmpp_idealMaximum power point current Impp_idealThe calculation formula of (2) is simplified. Step S4, introducing maximum power point voltage V under standard test condition of solar cellmpp_refAnd maximum power point current Impp_refDeducing the maximum power point voltage V of the solar batterymppMaximum power point current ImppAnd maximum power PmppApproximate linear estimation formula of (1).
Namely, the step four: simplifying a maximum power point parameter solving formula obtained under a general equivalent circuit model, neglecting a secondary part of the maximum power point parameter solving formula, and deducing an approximate calculation formula of maximum power point voltage and current under an ideal model;
step five: maximum power point voltage V under standard test condition of solar cellmpp_retAnd maximum power point current Impp_refAnd obtaining a maximum power point parameter approximate estimation formula under the general equivalent circuit model by using a general equivalent circuit model parameter solving formula and a maximum power point current and voltage approximate calculation formula under an ideal model.
The method comprises the following specific steps: as can be seen from equations (9) to (11), although the parameter solving formulas at the maximum power points do not include transcendental equations, the parameter solving formulas include many exponential operations and logarithmic operations, and therefore the solving formulas are not suitable for being used in the occasions requiring real-time performance or the occasions realized by embedded processors. Therefore, it is necessary to simplify these solving equations.
Get Iph、IoThe calculation formulas are respectively formula (12) and formula (13):
Figure BDA0001260645250000091
Figure BDA0001260645250000092
Iphis the photo-generated current of the solar cell; i isoIs a reverse saturation current; i isph_ref、Voc_refRespectively under the standard test conditions (standard)Conditional on reference solar intensity SrefIs 1000W/m2Reference temperature TrShort circuit current and open circuit voltage, mu, of the solar cell at 25 DEG CI、μVThe temperature coefficient of the short-circuit current and the temperature coefficient of the open-circuit voltage of the solar cell are respectively, S is the sunlight intensity, and T is the temperature.
Maximum power point voltage V under ideal circuit modelmpp_idealAnd maximum power point current Impp_idealApproximate calculations of equations (14) and (15) can be made:
Figure BDA0001260645250000101
Figure BDA0001260645250000102
in the pair formula (14)
Figure BDA0001260645250000103
The ones in (1) and (15)
Figure BDA0001260645250000104
Partial differential derivation is performed to obtain:
Figure BDA0001260645250000105
Figure BDA0001260645250000106
for crystalline silicon solar cells and thin film solar cells, the temperature coefficient of short circuit current is muIAnd open circuit voltage temperature coefficient muVIs generally at 10-3And the values of formulae (16) and (17) are in the order of 10-4Of the order of magnitude. Therefore, when estimating the parameter of the maximum power point of the solar cell, the influence of the temperature change on the corresponding part in the equations (16) and (17) can be ignored, that is, the corresponding part in the equations (16) and (17) is regarded as a constant when the temperature changes.
In order to reduce errors caused by various assumptions and approximations in the process of estimating the maximum power point parameter of the solar cell, the maximum power point voltage V under the standard test condition provided by a solar cell manufacturer is introduced in the estimation of the maximum power point parameter of the solar cellmpp_refAnd maximum power point current Impp_refAnd further deducing the maximum power point voltage V of the solar cellmppMaximum power point current ImppAnd maximum power PmppApproximate linear estimation formula of (1).
By T ═ Tr、S＝SrefV obtained by substituting formula (9) or formula (10)mpp、ImppIs namely Vmpp_ref、Impp_refThen V under other environmental conditionsmpp、ImppBy Vmpp_ref、Impp_refAnd V due to T, S changempp、ImppThe amount of change. That is, under standard conditions, can be obtained from formula (14) with T ═ TrWithout change, S was changed to investigate V under standard conditions resulting from S changempp_refCan obtain V caused by S changemppThe amplitude of the variation is
Figure BDA0001260645250000111
Keeping S unchanged, when S is SrefUnder the condition of (1), changing T, and researching maximum power point voltage V caused by T changemppRelative to V under standard conditionsmpp_refIn the case where V is obtainedmppLinearly varying with T, i.e. Δ Vmpp ═ μV(T-Tr) Therefore, the approximate solving formula of the maximum power point voltage of the solar battery obtained by combining the formula (9) is as follows:
Figure BDA0001260645250000112
further, from the formula (15), T is represented byrLeft unchanged, study S changes under standard conditions of light to ImppThe effect of (a) can be obtained,
Figure BDA0001260645250000113
keeping S as reference sunlight intensity, and examining I caused by T changemppIn this case I can be obtainedmppVaries linearly with T: Δ Impp ═ μI(T-Tr) Then I caused by the change in both S and T under standard conditionsmppThe variation relation is ImppThe approximate solution equation of (a):
Figure BDA0001260645250000121
there may then be:
Pmpp＝Vmpp·Imppformula (20)
Equations (18) to (20) are approximate linear estimation equations of the maximum power point parameter of the solar cell. The calculation amount of the approximate linear estimation formulas of the formulas (18) to (20) is greatly reduced relative to the accurate calculation formulas of the formulas (9) to (11). In practical engineering application, parameter solving methods can be selected according to parameter precision requirements and algorithm operand requirements, and solving formulas with different precisions are selected to solve engineering parameters.
The invention is described above with reference to the accompanying drawings. It is to be understood that the specific implementations of the invention are not limited in this respect. Various insubstantial improvements are made by adopting the method conception and the technical scheme of the invention; the present invention is not limited to the above embodiments, and can be modified in various ways.

Claims (1)

1. A method for solving parameters of a maximum power point of a solar cell is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing an ideal circuit model and a general circuit model of the solar cell;
step two: calculating a maximum power point parameter under an ideal circuit model;
step three: in a general equivalent circuit model, deriving a maximum power point parameter solving formula under the general equivalent circuit model according to a maximum power point parameter under an ideal circuit model and kirchhoff's law;
in the first step, the mathematical expression of the ideal circuit model of the solar cell is as follows:
Figure FDA0002520695640000011
the mathematical expression for a general equivalent circuit of a solar cell is:
Figure FDA0002520695640000012
in the formula: i isideal、VidealRespectively outputting current and voltage of the solar cell under an ideal circuit model; I. v is the output current and voltage of the solar cell under the general circuit model respectively; i isphIs the photo-generated current of the solar cell; i isoIs a reverse saturation current; q is the charge amount of one electron; k is the boltzmann constant; t is the temperature of the solar cell; n is an ideal factor for a solar cell; rs、RshThe circuit resistors are series and parallel circuit resistors inside the solar cell and are mainly used for representing current loss inside the cell;
in the second step, the method for solving the maximum power point parameter under the ideal circuit model comprises the following steps: and (3) derivation is carried out on the mathematical expression of the solar cell ideal circuit model to obtain the inverse relation of the output current of the solar cell with respect to the voltage under the ideal model:
Figure FDA0002520695640000013
the derivative of the current output by the solar cell with respect to voltage under an ideal circuit model is equal to the inverse of the ratio of the short circuit current to the open circuit voltage of the solar cell at the maximum power point position of the solar cell:
Figure FDA0002520695640000021
wherein Isc、VocShort circuit current and open circuit voltage for ideal solar cell(ii) a Thus, under an ideal model, the maximum power point voltage is obtained:
Figure FDA0002520695640000022
obtaining the current at the maximum power point under the ideal model according to the relation between the output voltage and the current of the solar battery under the ideal model:
Figure FDA0002520695640000023
short-circuit current IscPhoto-generated current I with solar cellphThe relationship between them is: i issc＝Iph；
Open circuit voltage VocPhoto-generated current I with solar cellphThe relationship between them is:
Figure FDA0002520695640000024
in the third step, when the ideal circuit model is at the maximum power point, the general equivalent circuit is also at the maximum power point, in the general equivalent circuit of the solar cell, the maximum power point current and the maximum power point voltage under the ideal model are combined, and simultaneously, the kirchhoff law is utilized to obtain the maximum power point voltage V under the general equivalent modelmppMaximum power point current ImppAnd maximum power PmppRespectively as follows:
Figure FDA0002520695640000025
Figure FDA0002520695640000026
Pmpp＝Vmpp·Impp；
further comprises the following steps: simplifying a maximum power point parameter solving formula obtained under a general equivalent circuit model, neglecting a secondary part of the maximum power point parameter solving formula, and deducing an approximate calculation formula of maximum power point voltage and current under an ideal model;
further comprises the following step five: maximum power point voltage V under standard test condition of solar cellmpp_refAnd maximum power point current Impp_refObtaining a maximum power point parameter approximate linear estimation formula under the general equivalent circuit model according to a parameter solving formula of the general equivalent circuit model and a maximum power point current and voltage approximate calculation formula under an ideal model;
photo-generated current I of solar cellphAnd reverse saturation current IoThe calculation formula is respectively:
Figure FDA0002520695640000031
Figure FDA0002520695640000032
Iph_ref、Voc_refshort-circuit current and open-circuit voltage, mu, of the solar cell under standard test conditionsI、μVRespectively the short-circuit current temperature coefficient and the open-circuit voltage temperature coefficient of the solar cell, and the temperature is T under the standard test conditionrThe intensity of sunlight is Sref；
Photo-generated current IphReverse saturation current IoThe approximate calculation formula of the maximum power point current and the voltage under the ideal model obtained by substituting the calculation formula into the maximum power point voltage current calculation formula under the ideal model respectively comprises the following steps:
Figure FDA0002520695640000033
Figure FDA0002520695640000041
step five, obtaining a maximum power point parameter approximate linear estimation formula under the general equivalent circuit model by a general equivalent circuit model parameter solving formula and a maximum power point current voltage approximate calculation formula under the ideal model, wherein the maximum power point parameter approximate linear estimation formula under the general equivalent circuit model is respectively as follows:
Figure FDA0002520695640000042
Figure FDA0002520695640000043
Pmpp＝Vmpp·Impp。
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